Before I got my first miniature, I bought a sulky and harness from a man who used to race horses in Florida. He mostly did regular-sized horses, but also got into the miniatures. When I met him, in OK, he no longer had big hroses, but was breeding miniatures for halter. He was older and getting tired and, to my knowledge, there is no miniature hrose racing anywhere around here; he sold me the sulky and harness. It is the kind with a quick hitch. I love it the setup; so easy to use with training and for quick excercise jaunts.
I think in Florida, many years ago, there were some for-real miniature horses races, but the only recent videos I've seen of it were for exhibition and it looked very disorganized. Some were trotting, some galloping. Every kind of vehicle. It looked more like a Land Run free-for-all than a horse race. Not a good advertisement for miniatures imho.
It would need to be set up in a more formal manner if anyone would take it seriously enough to train for it, and that would only happen if there were money to be made...